Temperatures tend to even out over time, i.e heat flows from hot to cold.
A drink at room temperature (say 20 degrees C) is significantly warmer than ice at 0 degrees C, this means that heat from the liquid will transfer into the ice until they are equilibrium.
If you used something like a cold whiskey stone this would decrease the temperature of the liquid and increase the temperature of the stone until they were the same. Ice is somewhat special in that it melts about 0 degrees C, this means it stays at 0 degrees until it has all melted so it is able to cool drinks considerably more than if it was just warming up without melting.
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